Read the following statements :
`S_(1)` : An object shall weigh more at pole than at equator when weighed by using a physical balance.
`S_(2)` : It shall weigh the same at pole and equator when weighed by using a physical balance.
`S_(3)` : It shall weigh the same at pole and equator when weighed by using a spring balance.
`S_(4)` : It shall weigh more at the pole than at equator when weighed using a spring balance.
Which of the above statements is/are correct ?

Options

A. `S_(1)` and `S_(2)`
B. `S_(1)` and `S_(4)`
C. `S_(2)` and `S_(3)`
D. `S_(2)` and `S_(4)`.

Answer

To solve the question, we need to analyze each statement regarding the weight of an object at the poles and the equator, considering the type of balance used for measurement.

### Step-by-Step Solution:

1. **Understanding Weight Measurement with a Physical Balance:**
- A physical balance compares the weights of two objects using a beam and a pivot. The weight measured is relative and depends on the gravitational force acting on both objects.
- Since the gravitational force changes with latitude (greater at the poles than at the equator), but both weights are affected equally, the balance will show that the weights are the same regardless of location.

**Conclusion for S1 and S2:**
- **S1:** An object shall weigh more at the pole than at the equator when weighed using a physical balance. **(Incorrect)**
- **S2:** It shall weigh the same at the pole and equator when weighed using a physical balance. **(Correct)**

2. **Understanding Weight Measurement with a Spring Balance:**
- A spring balance measures the weight of an object based on the force exerted by gravity on that object. The weight is directly proportional to the acceleration due to gravity.
- At the poles, the gravitational acceleration is higher than at the equator. Therefore, an object will weigh more at the pole than at the equator when measured with a spring balance.

**Conclusion for S3 and S4:**
- **S3:** It shall weigh the same at the pole and equator when weighed using a spring balance. **(Incorrect)**
- **S4:** It shall weigh more at the pole than at the equator when weighed using a spring balance. **(Correct)**

### Final Evaluation of Statements:
- **Correct Statements:** S2 and S4
- **Incorrect Statements:** S1 and S3

### Summary:
- **S1:** Incorrect
- **S2:** Correct
- **S3:** Incorrect
- **S4:** Correct